Question: Reduce to lowest terms: $- \dfrac{9}{2} \div \dfrac{9}{7} = {?}$
Explanation: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{9}{7}$ is $ \dfrac{7}{9}$ Therefore: $ - \dfrac{9}{2} \div \dfrac{9}{7} = - \dfrac{9}{2} \times \dfrac{7}{9} $ $ \phantom{- \dfrac{9}{2} \times \dfrac{7}{9}} = \dfrac{-9 \times 7}{2 \times 9} $ $ \phantom{- \dfrac{9}{2} \times \dfrac{7}{9}} = \dfrac{-63}{18} $ The numerator and denominator have a common divisor of $9$, so we can simplify: $ \dfrac{-63}{18} = \dfrac{-63 \div 9}{18 \div 9} = -\dfrac{7}{2} $